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Block #260,710

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 11/14/2013, 4:10:08 PM Ā· Difficulty 9.9763 Ā· 6,548,210 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
be174a807b9b4ce72710cf8fbb9f56ff70d229340f632d278abe90a27f30100a
View on Chainz ā†—

Height

#260,710

Difficulty

9.976312

Transactions

1

Size

1.61 KB

Version

2

Bits

09f9ef90

Nonce

204,191

Timestamp

11/14/2013, 4:10:08 PM

Confirmations

6,548,210

Mined by

ā›ļø faRlAU9KdB9rpz9LAxy9pEhEHibVcuo5XC6WMy

Merkle Root

7b6d913db33bdf3f47155bdcd72f8ca7c9ae754bb39637217e8fd18a79ae91e4
Transactions (1)
Coinbase7b6d913db33bdfā€¦8fd18a79ae91e4
1 in ā†’ 44 out10.0100 XPM1.52 KB
AU9KdB9rā€¦o5XC6WMyAFqKfjezā€¦qX9Ace3gAR6Lnfrdā€¦BmHL7S76APfZjrNuā€¦Wvzt6AFpAQtzUSwqā€¦htAuF3yC
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.

1.220 Ɨ 10ā¹āµ(96-digit number)
12202171285161998851ā€¦61832141989269731199
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
1.220 Ɨ 10ā¹āµ(96-digit number)
12202171285161998851ā€¦61832141989269731199
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
1.220 Ɨ 10ā¹āµ(96-digit number)
12202171285161998851ā€¦61832141989269731201
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
2.440 Ɨ 10ā¹āµ(96-digit number)
24404342570323997702ā€¦23664283978539462399
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
2.440 Ɨ 10ā¹āµ(96-digit number)
24404342570323997702ā€¦23664283978539462401
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
4.880 Ɨ 10ā¹āµ(96-digit number)
48808685140647995405ā€¦47328567957078924799
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
4.880 Ɨ 10ā¹āµ(96-digit number)
48808685140647995405ā€¦47328567957078924801
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
9.761 Ɨ 10ā¹āµ(96-digit number)
97617370281295990811ā€¦94657135914157849599
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
9.761 Ɨ 10ā¹āµ(96-digit number)
97617370281295990811ā€¦94657135914157849601
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
1.952 Ɨ 10ā¹ā¶(97-digit number)
19523474056259198162ā€¦89314271828315699199
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
1.952 Ɨ 10ā¹ā¶(97-digit number)
19523474056259198162ā€¦89314271828315699201
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:57,715,415 XPMĀ·at block #6,808,919 Ā· updates every 60s
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