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Block #61,694

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 2:51:27 PM Β· Difficulty 8.9740 Β· 6,747,593 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
a922974f04f35db2b9d6e7b177724fa13e7434ea835cca71381ae5feef34f940
View on Chainz β†—

Height

#61,694

Difficulty

8.973992

Transactions

1

Size

204 B

Version

2

Bits

08f95786

Nonce

105

Timestamp

7/18/2013, 2:51:27 PM

Confirmations

6,747,593

Merkle Root

8ef271043530c35cf4c81340dd8b73cc7a28c4fb19b487182a6c1c011d06c85a
Transactions (1)
Coinbase8ef271043530c3…6c1c011d06c85a
1 in β†’ 1 out12.4000 XPM110 B
AXY6feyt…oghmWWGf
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.493 Γ— 10¹⁰⁴(105-digit number)
24931372773577173360…93986343102715562820
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.493 Γ— 10¹⁰⁴(105-digit number)
24931372773577173360…93986343102715562819
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.493 Γ— 10¹⁰⁴(105-digit number)
24931372773577173360…93986343102715562821
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.986 Γ— 10¹⁰⁴(105-digit number)
49862745547154346721…87972686205431125639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.986 Γ— 10¹⁰⁴(105-digit number)
49862745547154346721…87972686205431125641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
9.972 Γ— 10¹⁰⁴(105-digit number)
99725491094308693442…75945372410862251279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.972 Γ— 10¹⁰⁴(105-digit number)
99725491094308693442…75945372410862251281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.994 Γ— 10¹⁰⁡(106-digit number)
19945098218861738688…51890744821724502559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.994 Γ— 10¹⁰⁡(106-digit number)
19945098218861738688…51890744821724502561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.989 Γ— 10¹⁰⁡(106-digit number)
39890196437723477376…03781489643449005119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 61694

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock a922974f04f35db2b9d6e7b177724fa13e7434ea835cca71381ae5feef34f940

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #61,694 on Chainz β†—
Circulating Supply:57,718,365 XPMΒ·at block #6,809,286 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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