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Block #51,438

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 5:47:45 AM Β· Difficulty 8.8984 Β· 6,759,710 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
52fc423683e7e7064351ac3c9ce37877b3230a627a508dd6e6956f7493819a82
View on Chainz β†—

Height

#51,438

Difficulty

8.898428

Transactions

1

Size

202 B

Version

2

Bits

08e5ff5e

Nonce

847

Timestamp

7/16/2013, 5:47:45 AM

Confirmations

6,759,710

Mined by

⛏️ P2SHAX85bWR1s13thBJxnmv7Zr62AvX2GwLbPj

Merkle Root

65d6bd9ec63c6bb558397d74caddb5910fcfb6fa6f5b9f0c9265dccbb11c37a8
Transactions (1)
Coinbase65d6bd9ec63c6b…65dccbb11c37a8
1 in β†’ 1 out12.6100 XPM110 B
AX85bWR1…X2GwLbPj
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.

8.188 Γ— 10⁹⁸(99-digit number)
81884046825158800079…55662334037518156129
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
8.188 Γ— 10⁹⁸(99-digit number)
81884046825158800079…55662334037518156129
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.188 Γ— 10⁹⁸(99-digit number)
81884046825158800079…55662334037518156131
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
1.637 Γ— 10⁹⁹(100-digit number)
16376809365031760015…11324668075036312259
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.637 Γ— 10⁹⁹(100-digit number)
16376809365031760015…11324668075036312261
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
3.275 Γ— 10⁹⁹(100-digit number)
32753618730063520031…22649336150072624519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.275 Γ— 10⁹⁹(100-digit number)
32753618730063520031…22649336150072624521
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
6.550 Γ— 10⁹⁹(100-digit number)
65507237460127040063…45298672300145249039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.550 Γ— 10⁹⁹(100-digit number)
65507237460127040063…45298672300145249041
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
1.310 Γ— 10¹⁰⁰(101-digit number)
13101447492025408012…90597344600290498079
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:57,733,294 XPMΒ·at block #6,811,147 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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