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Block #465,054

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 3/29/2014, 4:55:51 AM Ā· Difficulty 10.4228 Ā· 6,345,279 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
84c0d724689127e6cccfbfdf203360b62f4c8a59355207069e82a79ab65a545b
View on Chainz ā†—

Height

#465,054

Difficulty

10.422812

Transactions

1

Size

901 B

Version

2

Bits

0a6c3d6c

Nonce

152,299

Timestamp

3/29/2014, 4:55:51 AM

Confirmations

6,345,279

Mined by

ā›ļø aS6T-AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f8a205a6a9d3c936a71cefb217382c0158c14bc95763f1d28ecd7ef35ecca9a6
Transactions (1)
Coinbasef8a205a6a9d3c9ā€¦cd7ef35ecca9a6
1 in ā†’ 22 out9.1900 XPM811 B
AQvZBsUoā€¦hppgRZTJANNg88pGā€¦ppn21sTeAQ8QAT3Jā€¦rCFKuVbRATKK7iFzā€¦wZm46KN1ALqxX1WAā€¦hsKjbnXn
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.918 Ɨ 10ā¹ā“(95-digit number)
59182874261263119544ā€¦55756034694342514389
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ 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 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
5.918 Ɨ 10ā¹ā“(95-digit number)
59182874261263119544ā€¦55756034694342514389
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
5.918 Ɨ 10ā¹ā“(95-digit number)
59182874261263119544ā€¦55756034694342514391
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
1.183 Ɨ 10ā¹āµ(96-digit number)
11836574852252623908ā€¦11512069388685028779
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
1.183 Ɨ 10ā¹āµ(96-digit number)
11836574852252623908ā€¦11512069388685028781
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
2.367 Ɨ 10ā¹āµ(96-digit number)
23673149704505247817ā€¦23024138777370057559
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
2.367 Ɨ 10ā¹āµ(96-digit number)
23673149704505247817ā€¦23024138777370057561
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
4.734 Ɨ 10ā¹āµ(96-digit number)
47346299409010495635ā€¦46048277554740115119
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
4.734 Ɨ 10ā¹āµ(96-digit number)
47346299409010495635ā€¦46048277554740115121
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
9.469 Ɨ 10ā¹āµ(96-digit number)
94692598818020991271ā€¦92096555109480230239
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
9.469 Ɨ 10ā¹āµ(96-digit number)
94692598818020991271ā€¦92096555109480230241
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)

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 ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜…ā˜†ā˜†ā˜†
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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” 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 āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,726,744 XPMĀ·at block #6,810,332 Ā· updates every 60s
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