Block #2,619,053

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/18/2018, 5:15:30 AM · Difficulty 11.2447 · 4,188,440 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

569fdba73947b6c6b0e683319e314427f2d46fbb29e2e3d29ab411fb93758127

View on Chainz ↗

Height

#2,619,053

Difficulty

11.244692

Transactions

Size

33.68 KB

Version

Bits

0b3ea41c

Nonce

1,460,093,888

Timestamp

4/18/2018, 5:15:30 AM

Confirmations

4,188,440

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

c25b242ed0a796628717a3306c7fea51c2016f0bd45f63346a256e83cbc3d625

Transactions (5)

Coinbase986f494a109a35…9894229481a95c

1 in → 1 out8.2600 XPM109 B

Adqah8zh…1WwoHJ9t

3272103cfee8e1…481add3af29a58

222 in → 2 out200.0100 XPM32.17 KB

ALPF8J52…Hjw4BMsG ARiPrNwg…YHYCY5wS

1513ed10583ff9…f2fc81ff893661

1 in → 2 out7.9200 XPM191 B

AT7Mb2v6…6BJWUbU1 AWp4iAg7…FUBLEm8x

fa9c572592e366…3b80914b5f52e9

1 in → 2 out7.9200 XPM193 B

AaaBa4PN…RF3M5qVE AdMtrT7m…zgeRbAcK

94ad1f1060c7a5…2924b96558b774

6 in → 2 out5.0902 XPM966 B

AaZQbN1o…Vayvwn2q AKBxhYmY…4XGb9PCf

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.

2.940 × 10⁹⁴(95-digit number)

29402718856906060394…67999578380318526639

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

2.940 × 10⁹⁴(95-digit number)

29402718856906060394…67999578380318526639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.940 × 10⁹⁴(95-digit number)

29402718856906060394…67999578380318526641

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

5.880 × 10⁹⁴(95-digit number)

58805437713812120789…35999156760637053279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.880 × 10⁹⁴(95-digit number)

58805437713812120789…35999156760637053281

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

1.176 × 10⁹⁵(96-digit number)

11761087542762424157…71998313521274106559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.176 × 10⁹⁵(96-digit number)

11761087542762424157…71998313521274106561

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

2.352 × 10⁹⁵(96-digit number)

23522175085524848315…43996627042548213119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.352 × 10⁹⁵(96-digit number)

23522175085524848315…43996627042548213121

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

4.704 × 10⁹⁵(96-digit number)

47044350171049696631…87993254085096426239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.704 × 10⁹⁵(96-digit number)

47044350171049696631…87993254085096426241

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

9.408 × 10⁹⁵(96-digit number)

94088700342099393262…75986508170192852479

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 #2,619,053

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