Block #2,719,002

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/24/2018, 7:36:50 AM · Difficulty 11.6135 · 4,122,836 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a2c280bd214ea8c4ebe0efc2abcd30a4f144cec3713bfa55dea3f26f3053ce1d

View on Chainz ↗

Height

#2,719,002

Difficulty

11.613497

Transactions

Size

1.48 KB

Version

Bits

0b9d0e20

Nonce

750,990,470

Timestamp

6/24/2018, 7:36:50 AM

Confirmations

4,122,836

Mined by

⛏️ P2SHALQGpaT6bUeDR1X73XRmMe4Z6w9dLVU1B9

Merkle Root

e4f05f29e71cb762254f68cb183ea2c64fbdc17b8c62c1f23f9985acb59cffc0

Transactions (4)

Coinbasead90f492be8a3e…b42b07d9ad5896

1 in → 1 out7.4300 XPM109 B

ALQGpaT6…9dLVU1B9

5a6e31826eab24…f0af7b7e9757de

2 in → 2 out12.1900 XPM341 B

AKfRXb6E…WzLM8r1d AQDFkcwX…xc72nANc

56506687ea9d40…1ccbccf4038381

5 in → 1 out10.0000 XPM748 B

APVKWthF…PMMxwRoz

ca588f34a7efb4…2fcce8d8db7234

1 in → 2 out0.8430 XPM226 B

Ad8PfezF…USss5Max Aa8JjQQJ…xC5QuG6W

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.

8.482 × 10⁹⁵(96-digit number)

84820014969915895646…72564146408085839999

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

8.482 × 10⁹⁵(96-digit number)

84820014969915895646…72564146408085839999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.482 × 10⁹⁵(96-digit number)

84820014969915895646…72564146408085840001

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

1.696 × 10⁹⁶(97-digit number)

16964002993983179129…45128292816171679999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.696 × 10⁹⁶(97-digit number)

16964002993983179129…45128292816171680001

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

3.392 × 10⁹⁶(97-digit number)

33928005987966358258…90256585632343359999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.392 × 10⁹⁶(97-digit number)

33928005987966358258…90256585632343360001

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

6.785 × 10⁹⁶(97-digit number)

67856011975932716517…80513171264686719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.785 × 10⁹⁶(97-digit number)

67856011975932716517…80513171264686720001

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

1.357 × 10⁹⁷(98-digit number)

13571202395186543303…61026342529373439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.357 × 10⁹⁷(98-digit number)

13571202395186543303…61026342529373440001

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

2.714 × 10⁹⁷(98-digit number)

27142404790373086606…22052685058746879999

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 #2,719,002

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