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Block #259,539

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/13/2013, 4:36:48 PM Β· Difficulty 9.9774 Β· 6,553,195 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b32bc2420f538d605b92f68565826c3b7034c3a2307202b18533ad561e3222b0
View on Chainz β†—

Height

#259,539

Difficulty

9.977378

Transactions

2

Size

869 B

Version

2

Bits

09fa3578

Nonce

147,480

Timestamp

11/13/2013, 4:36:48 PM

Confirmations

6,553,195

Mined by

⛏️ P2SHAGupqPiKYXQAcMSXWd2JNSKfVrg63rypjr

Merkle Root

7adaae22ff25c5ebefc2beaf406000661b4ff01cebd528e2f917424a43169190
Transactions (2)
Coinbase8860c2e040dba4…9ed4a32c4a4cab
1 in β†’ 1 out10.0400 XPM109 B
AGupqPiK…g63rypjr
51933e5ecdbf38…da5aa2673c59f8
4 in β†’ 2 out103.7822 XPM670 B
AcpM8qYo…rWfzrm7sAZdmkNt9…Dk8ffFeU
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.

1.899 Γ— 10⁹⁡(96-digit number)
18991367213411856857…86414447378467191039
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
1.899 Γ— 10⁹⁡(96-digit number)
18991367213411856857…86414447378467191039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.899 Γ— 10⁹⁡(96-digit number)
18991367213411856857…86414447378467191041
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
3.798 Γ— 10⁹⁡(96-digit number)
37982734426823713714…72828894756934382079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.798 Γ— 10⁹⁡(96-digit number)
37982734426823713714…72828894756934382081
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
7.596 Γ— 10⁹⁡(96-digit number)
75965468853647427429…45657789513868764159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.596 Γ— 10⁹⁡(96-digit number)
75965468853647427429…45657789513868764161
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
1.519 Γ— 10⁹⁢(97-digit number)
15193093770729485485…91315579027737528319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.519 Γ— 10⁹⁢(97-digit number)
15193093770729485485…91315579027737528321
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
3.038 Γ— 10⁹⁢(97-digit number)
30386187541458970971…82631158055475056639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.038 Γ— 10⁹⁢(97-digit number)
30386187541458970971…82631158055475056641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.077 Γ— 10⁹⁢(97-digit number)
60772375082917941943…65262316110950113279
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,745,913 XPMΒ·at block #6,812,733 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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