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Block #113,469

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/12/2013, 1:41:46 PM Β· Difficulty 9.7325 Β· 6,692,573 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
317919795f49d9f2dd637dec020343cda1f4c752743dde63baab0fc7afd160f7
View on Chainz β†—

Height

#113,469

Difficulty

9.732516

Transactions

1

Size

200 B

Version

2

Bits

09bb8624

Nonce

505,519

Timestamp

8/12/2013, 1:41:46 PM

Confirmations

6,692,573

Merkle Root

c3ac3601dc62b340984d5b7181ee8360ef4e08276ac0310d9063879cb3760115
Transactions (1)
Coinbasec3ac3601dc62b3…63879cb3760115
1 in β†’ 1 out10.5400 XPM109 B
AaLrWjpu…QmdcRbaT
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.

2.302 Γ— 10⁹⁸(99-digit number)
23023184603348537758…91004650484522987520
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
2.302 Γ— 10⁹⁸(99-digit number)
23023184603348537758…91004650484522987519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.302 Γ— 10⁹⁸(99-digit number)
23023184603348537758…91004650484522987521
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
4.604 Γ— 10⁹⁸(99-digit number)
46046369206697075516…82009300969045975039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.604 Γ— 10⁹⁸(99-digit number)
46046369206697075516…82009300969045975041
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
9.209 Γ— 10⁹⁸(99-digit number)
92092738413394151032…64018601938091950079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.209 Γ— 10⁹⁸(99-digit number)
92092738413394151032…64018601938091950081
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
1.841 Γ— 10⁹⁹(100-digit number)
18418547682678830206…28037203876183900159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.841 Γ— 10⁹⁹(100-digit number)
18418547682678830206…28037203876183900161
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
3.683 Γ— 10⁹⁹(100-digit number)
36837095365357660413…56074407752367800319
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 113469

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 317919795f49d9f2dd637dec020343cda1f4c752743dde63baab0fc7afd160f7

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 #113,469 on Chainz β†—
Circulating Supply:57,692,417 XPMΒ·at block #6,806,041 Β· updates every 60s
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