XPM Prime Explorer symbol
XPMPrime Explorer

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· 6,746,436 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

6,746,436

Mined by

⛏️ P2SHAXY6feytV6ZxBQJFLAbLwdMRw9oghmWWGf

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…93986343102715562819
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,709,081 XPMΒ·at block #6,808,129 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy