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Block #183,426

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/28/2013, 12:12:27 AM Β· Difficulty 9.8583 Β· 6,625,745 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5fbabd4d618282ee02e3cbad1b061d6063527bf308dd18dcdc3c8b39241bcd03
View on Chainz β†—

Height

#183,426

Difficulty

9.858270

Transactions

2

Size

427 B

Version

2

Bits

09dbb797

Nonce

28,227

Timestamp

9/28/2013, 12:12:27 AM

Confirmations

6,625,745

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

1e89b052a2a35313f0c77098d15bc5e281f3d18ae39a2039806f4bb42e5b378b
Transactions (2)
Coinbase706fa1162c66a6…cbd28a454d94ac
1 in β†’ 1 out10.2800 XPM109 B
AWbQMT1U…8Pt4ow7J
fc91d19b0af70b…a64c584bcd3888
1 in β†’ 2 out201.1591 XPM227 B
AU51fQpg…v7HJhFQQAFqDj4vn…D3w8GBCw
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.

5.871 Γ— 10⁹⁷(98-digit number)
58713213304423847969…32826156540743577599
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
5.871 Γ— 10⁹⁷(98-digit number)
58713213304423847969…32826156540743577599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.871 Γ— 10⁹⁷(98-digit number)
58713213304423847969…32826156540743577601
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
1.174 Γ— 10⁹⁸(99-digit number)
11742642660884769593…65652313081487155199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.174 Γ— 10⁹⁸(99-digit number)
11742642660884769593…65652313081487155201
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
2.348 Γ— 10⁹⁸(99-digit number)
23485285321769539187…31304626162974310399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.348 Γ— 10⁹⁸(99-digit number)
23485285321769539187…31304626162974310401
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
4.697 Γ— 10⁹⁸(99-digit number)
46970570643539078375…62609252325948620799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.697 Γ— 10⁹⁸(99-digit number)
46970570643539078375…62609252325948620801
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
9.394 Γ— 10⁹⁸(99-digit number)
93941141287078156750…25218504651897241599
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:57,717,431 XPMΒ·at block #6,809,170 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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