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Block #403,818

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 2/14/2014, 10:32:18 AM Ā· Difficulty 10.4320 Ā· 6,402,895 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3a9a78d49994916b0d62ba31801a111d753b1c3053b67e7fed7a90aaf976380f
View on Chainz ā†—

Height

#403,818

Difficulty

10.431967

Transactions

1

Size

901 B

Version

2

Bits

0a6e955e

Nonce

8,013

Timestamp

2/14/2014, 10:32:18 AM

Confirmations

6,402,895

Mined by

ā›ļø jAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

950a7a4317f8a0c9c456571dc53d057b9921b98f4b9f691c0d4ae066c9eca4fc
Transactions (1)
Coinbase950a7a4317f8a0ā€¦4ae066c9eca4fc
1 in ā†’ 22 out9.1700 XPM811 B
AQvZBsUoā€¦hppgRZTJAac9Hjdgā€¦P4ktypc3AYtDvcGsā€¦VuAcA7m7AYRvXuTrā€¦CkbwFeLYAGKhfQo2ā€¦h7fBXLX6
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.

2.472 Ɨ 10ā¹āµ(96-digit number)
24726965543189680335ā€¦70572182883536723839
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
2.472 Ɨ 10ā¹āµ(96-digit number)
24726965543189680335ā€¦70572182883536723839
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
2.472 Ɨ 10ā¹āµ(96-digit number)
24726965543189680335ā€¦70572182883536723841
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
4.945 Ɨ 10ā¹āµ(96-digit number)
49453931086379360670ā€¦41144365767073447679
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
4.945 Ɨ 10ā¹āµ(96-digit number)
49453931086379360670ā€¦41144365767073447681
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
9.890 Ɨ 10ā¹āµ(96-digit number)
98907862172758721341ā€¦82288731534146895359
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
9.890 Ɨ 10ā¹āµ(96-digit number)
98907862172758721341ā€¦82288731534146895361
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
1.978 Ɨ 10ā¹ā¶(97-digit number)
19781572434551744268ā€¦64577463068293790719
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
1.978 Ɨ 10ā¹ā¶(97-digit number)
19781572434551744268ā€¦64577463068293790721
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
3.956 Ɨ 10ā¹ā¶(97-digit number)
39563144869103488536ā€¦29154926136587581439
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
3.956 Ɨ 10ā¹ā¶(97-digit number)
39563144869103488536ā€¦29154926136587581441
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:57,697,802 XPMĀ·at block #6,806,712 Ā· updates every 60s
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