Block #712,257

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/8/2014, 11:34:35 AM · Difficulty 10.9558 · 6,097,893 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

53e01fe76cf18ee6abd1fa423e8912212b025a512086df743bcf75936f5ae4d4

View on Chainz ↗

Height

#712,257

Difficulty

10.955840

Transactions

Size

3.60 KB

Version

Bits

0af4b1ea

Nonce

134,950,245

Timestamp

9/8/2014, 11:34:35 AM

Confirmations

6,097,893

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a45460d32b959d9af685034b102540e3c4b8f82cbfe68cf16e9b8626fa94e82f

Transactions (2)

Coinbase203a85ef20b80f…fc408207e9bce9

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

1a5c9726e768c7…c817b600c2de32

23 in → 2 out500.0101 XPM3.40 KB

AJjnK9uC…VreFquR4 AWV42MRw…QPNZKycS

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.721 × 10⁹⁹(100-digit number)

77211923410451930319…21423790150826721279

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

7.721 × 10⁹⁹(100-digit number)

77211923410451930319…21423790150826721279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.721 × 10⁹⁹(100-digit number)

77211923410451930319…21423790150826721281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.544 × 10¹⁰⁰(101-digit number)

15442384682090386063…42847580301653442559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.544 × 10¹⁰⁰(101-digit number)

15442384682090386063…42847580301653442561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.088 × 10¹⁰⁰(101-digit number)

30884769364180772127…85695160603306885119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.088 × 10¹⁰⁰(101-digit number)

30884769364180772127…85695160603306885121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

6.176 × 10¹⁰⁰(101-digit number)

61769538728361544255…71390321206613770239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.176 × 10¹⁰⁰(101-digit number)

61769538728361544255…71390321206613770241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.235 × 10¹⁰¹(102-digit number)

12353907745672308851…42780642413227540479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.235 × 10¹⁰¹(102-digit number)

12353907745672308851…42780642413227540481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.470 × 10¹⁰¹(102-digit number)

24707815491344617702…85561284826455080959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #712,257

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