Block #1,411,613

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2016, 12:27:23 PM · Difficulty 10.8057 · 5,415,789 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01a9f53c3ea83314884ad7061b4557aad01f00f2ad8e683adc6734a941bd9622

View on Chainz ↗

Height

#1,411,613

Difficulty

10.805719

Transactions

Size

2.00 KB

Version

Bits

0ace43a2

Nonce

96,952,593

Timestamp

1/13/2016, 12:27:23 PM

Confirmations

5,415,789

Mined by

⛏️ P2SHAUQRVzTmtNjThmyHcBVm1tRbHPZSwQKEKw

Merkle Root

014f02842d85d06c27c7127194cce5e444bc86b973539c3b3a14412d826b51de

Transactions (2)

Coinbaseec8977446299b2…dee1b92ad37cf1

1 in → 1 out8.5700 XPM109 B

AUQRVzTm…ZSwQKEKw

0c675fcc1ea5fd…36e150a2510641

12 in → 2 out63.5832 XPM1.81 KB

AQHE5e6H…xDwU3vYU AVS85B1j…sgySaphb

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.

5.327 × 10⁹³(94-digit number)

53271532647984875718…04559708884462284399

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

5.327 × 10⁹³(94-digit number)

53271532647984875718…04559708884462284399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.327 × 10⁹³(94-digit number)

53271532647984875718…04559708884462284401

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

1.065 × 10⁹⁴(95-digit number)

10654306529596975143…09119417768924568799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.065 × 10⁹⁴(95-digit number)

10654306529596975143…09119417768924568801

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

2.130 × 10⁹⁴(95-digit number)

21308613059193950287…18238835537849137599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.130 × 10⁹⁴(95-digit number)

21308613059193950287…18238835537849137601

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

4.261 × 10⁹⁴(95-digit number)

42617226118387900574…36477671075698275199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.261 × 10⁹⁴(95-digit number)

42617226118387900574…36477671075698275201

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

8.523 × 10⁹⁴(95-digit number)

85234452236775801149…72955342151396550399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.523 × 10⁹⁴(95-digit number)

85234452236775801149…72955342151396550401

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,411,613

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