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Block #54,817

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 10:24:50 PM Β· Difficulty 8.9368 Β· 6,752,363 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aec7590c37137023cfca8a9ae15771ed01655855365c0ca811f95e89822f25f0
View on Chainz β†—

Height

#54,817

Difficulty

8.936764

Transactions

1

Size

198 B

Version

2

Bits

08efcfcc

Nonce

738

Timestamp

7/16/2013, 10:24:50 PM

Confirmations

6,752,363

Mined by

⛏️ P2SHAXY6feytV6ZxBQJFLAbLwdMRw9oghmWWGf

Merkle Root

215ad86625f2b84e21e67fa95f84e0473e350f208a0055a55270445c6af2d00d
Transactions (1)
Coinbase215ad86625f2b8…70445c6af2d00d
1 in β†’ 1 out12.5000 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— 10⁹⁰(91-digit number)
24933696236608953488…75579238403795563519
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— 10⁹⁰(91-digit number)
24933696236608953488…75579238403795563519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.493 Γ— 10⁹⁰(91-digit number)
24933696236608953488…75579238403795563521
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— 10⁹⁰(91-digit number)
49867392473217906977…51158476807591127039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.986 Γ— 10⁹⁰(91-digit number)
49867392473217906977…51158476807591127041
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
9.973 Γ— 10⁹⁰(91-digit number)
99734784946435813954…02316953615182254079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.973 Γ— 10⁹⁰(91-digit number)
99734784946435813954…02316953615182254081
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— 10⁹¹(92-digit number)
19946956989287162790…04633907230364508159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.994 Γ— 10⁹¹(92-digit number)
19946956989287162790…04633907230364508161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,701,451 XPMΒ·at block #6,807,179 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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