Block #3,337,997

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/2/2019, 4:38:35 PM · Difficulty 11.0000 · 3,504,313 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c72229cebb8a95697f0855580fa61d539fce56c1f741f2107df6a90b6b736bf

View on Chainz ↗

Height

#3,337,997

Difficulty

11.000000

Transactions

Size

427 B

Version

Bits

0b000000

Nonce

1,617,396,922

Timestamp

9/2/2019, 4:38:35 PM

Confirmations

3,504,313

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMz Visit pool ↗

Merkle Root

e84b04bd6c53ac9a3e6203a6e2c9e34f3a4676fd01b40bb844009bc15f344329

Transactions (2)

Coinbase1f190b66067caf…873c8d1a4ff37a

1 in → 1 out8.2600 XPM110 B

AXfJqzUb…HXeXmjMz

bd706c31a55094…14b00a0e8a3b49

1 in → 2 out139.7793 XPM227 B

APQ9gg1V…H4v8MyZ4 AMLggddy…HpikgH98

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.

4.947 × 10⁹⁵(96-digit number)

49473532566251087043…45397064248964767999

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

4.947 × 10⁹⁵(96-digit number)

49473532566251087043…45397064248964767999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.947 × 10⁹⁵(96-digit number)

49473532566251087043…45397064248964768001

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

9.894 × 10⁹⁵(96-digit number)

98947065132502174087…90794128497929535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.894 × 10⁹⁵(96-digit number)

98947065132502174087…90794128497929536001

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

1.978 × 10⁹⁶(97-digit number)

19789413026500434817…81588256995859071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.978 × 10⁹⁶(97-digit number)

19789413026500434817…81588256995859072001

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

3.957 × 10⁹⁶(97-digit number)

39578826053000869634…63176513991718143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.957 × 10⁹⁶(97-digit number)

39578826053000869634…63176513991718144001

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

7.915 × 10⁹⁶(97-digit number)

79157652106001739269…26353027983436287999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.915 × 10⁹⁶(97-digit number)

79157652106001739269…26353027983436288001

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

1.583 × 10⁹⁷(98-digit number)

15831530421200347853…52706055966872575999

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 #3,337,997

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