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Block #260,591

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/14/2013, 11:38:43 AM Β· Difficulty 9.9770 Β· 6,570,004 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
706be552a0df70fab9d19f59e6d80f0c55f84d0745b831998233fba4c1abd144
View on Chainz β†—

Height

#260,591

Difficulty

9.977018

Transactions

2

Size

3.57 KB

Version

2

Bits

09fa1ddf

Nonce

203,722

Timestamp

11/14/2013, 11:38:43 AM

Confirmations

6,570,004

Mined by

⛏️ P2SHAc9x2WG78p4t67TePRLcUaxs7j9hN8Lrmy

Merkle Root

822091da9f2390c777a129f7f0475f065dbcddc187505e5bd8459b5e4dbfa423
Transactions (2)
Coinbase0d478fec1487f0…0da5d953d107d8
1 in β†’ 1 out10.0715 XPM109 B
Ac9x2WG7…9hN8Lrmy
9ead56c0f57cb4…9d9eba0fc9359d
23 in β†’ 1 out2.3800 XPM3.37 KB
ARyStGH2…oTd9knZa
Prime Chain Origin

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

1.727 Γ— 10¹⁰²(103-digit number)
17277603252420610151…51480117135718753279
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.727 Γ— 10¹⁰²(103-digit number)
17277603252420610151…51480117135718753279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.727 Γ— 10¹⁰²(103-digit number)
17277603252420610151…51480117135718753281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.455 Γ— 10¹⁰²(103-digit number)
34555206504841220302…02960234271437506559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.455 Γ— 10¹⁰²(103-digit number)
34555206504841220302…02960234271437506561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
6.911 Γ— 10¹⁰²(103-digit number)
69110413009682440604…05920468542875013119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.911 Γ— 10¹⁰²(103-digit number)
69110413009682440604…05920468542875013121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.382 Γ— 10¹⁰³(104-digit number)
13822082601936488120…11840937085750026239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.382 Γ— 10¹⁰³(104-digit number)
13822082601936488120…11840937085750026241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.764 Γ— 10¹⁰³(104-digit number)
27644165203872976241…23681874171500052479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,888,881 XPMΒ·at block #6,830,594 Β· updates every 60s
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