Block #3,233,619

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/20/2019, 5:54:14 PM · Difficulty 10.9960 · 3,606,990 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dca409c9872100df57bc0ca578572a97205b971d4e1ec44295a47ba7dd459cde

View on Chainz ↗

Height

#3,233,619

Difficulty

10.996049

Transactions

Size

2.02 KB

Version

Bits

0afefd0d

Nonce

1,186,981,988

Timestamp

6/20/2019, 5:54:14 PM

Confirmations

3,606,990

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

6a7c79a65a3deecbf14b19d05f5cfa182e12e4d34ba96008e6362ca5e24940ab

Transactions (5)

Coinbasef5eaa210b79217…4d69a364a4354d

1 in → 1 out8.3000 XPM109 B

ARbm48qR…9xQc8DBX

86524151cee163…fc7b8af6dab0aa

3 in → 2 out15.7115 XPM489 B

AbXwmGxD…4XXYP765 AHRiuNWd…x34SS1Jh

239bc192486208…2eaea005b317d6

5 in → 2 out15.2156 XPM785 B

AdGFnV3a…o6n2zX3x AbXwmGxD…4XXYP765

2db8ab9271db23…e05314f13dbe0c

1 in → 2 out4.9214 XPM227 B

AbXwmGxD…4XXYP765 AJtQNmM4…XBRjaQ6m

9733670a02e512…2ce0ff7a29f41c

2 in → 2 out1.0615 XPM374 B

AXrr1C53…dFRcw5HZ AbXwmGxD…4XXYP765

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.

6.419 × 10⁹¹(92-digit number)

64196510635457375021…08080848207152471499

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

6.419 × 10⁹¹(92-digit number)

64196510635457375021…08080848207152471499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.419 × 10⁹¹(92-digit number)

64196510635457375021…08080848207152471501

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

1.283 × 10⁹²(93-digit number)

12839302127091475004…16161696414304942999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.283 × 10⁹²(93-digit number)

12839302127091475004…16161696414304943001

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

2.567 × 10⁹²(93-digit number)

25678604254182950008…32323392828609885999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.567 × 10⁹²(93-digit number)

25678604254182950008…32323392828609886001

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

5.135 × 10⁹²(93-digit number)

51357208508365900016…64646785657219771999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.135 × 10⁹²(93-digit number)

51357208508365900016…64646785657219772001

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

1.027 × 10⁹³(94-digit number)

10271441701673180003…29293571314439543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.027 × 10⁹³(94-digit number)

10271441701673180003…29293571314439544001

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

2.054 × 10⁹³(94-digit number)

20542883403346360006…58587142628879087999

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 #3,233,619

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