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Block #561,736

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/25/2014, 4:55:18 PM Β· Difficulty 10.9654 Β· 6,232,798 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5a4f8933326f1f49b0729a4ee3a5a3b1dca18031e872ce844a312f8d0060b2be
View on Chainz β†—

Height

#561,736

Difficulty

10.965448

Transactions

2

Size

435 B

Version

2

Bits

0af72794

Nonce

1,802,827,254

Timestamp

5/25/2014, 4:55:18 PM

Confirmations

6,232,798

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

14dad9a06bde0097bebc39157e0cdaf92c68dc441ba01e598b2fa0c8cecaa2e4
Transactions (2)
Coinbasede29d1b4fdcbe8…5d340ca7658444
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
acb0af9082b054…3fb9d4a39ed292
1 in β†’ 3 out8.3000 XPM227 B
AL9UZuKj…g3Q3eciVAeKNrjNj…1NEq95TaAHbu8w6V…13P7BwSQ
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.

1.874 Γ— 10⁹⁹(100-digit number)
18743871991557818526…62891762292772679679
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
1.874 Γ— 10⁹⁹(100-digit number)
18743871991557818526…62891762292772679679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.874 Γ— 10⁹⁹(100-digit number)
18743871991557818526…62891762292772679681
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
3.748 Γ— 10⁹⁹(100-digit number)
37487743983115637052…25783524585545359359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.748 Γ— 10⁹⁹(100-digit number)
37487743983115637052…25783524585545359361
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
7.497 Γ— 10⁹⁹(100-digit number)
74975487966231274104…51567049171090718719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.497 Γ— 10⁹⁹(100-digit number)
74975487966231274104…51567049171090718721
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
1.499 Γ— 10¹⁰⁰(101-digit number)
14995097593246254820…03134098342181437439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.499 Γ— 10¹⁰⁰(101-digit number)
14995097593246254820…03134098342181437441
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
2.999 Γ— 10¹⁰⁰(101-digit number)
29990195186492509641…06268196684362874879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.999 Γ— 10¹⁰⁰(101-digit number)
29990195186492509641…06268196684362874881
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
5.998 Γ— 10¹⁰⁰(101-digit number)
59980390372985019283…12536393368725749759
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:57,600,312 XPMΒ·at block #6,794,533 Β· updates every 60s
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