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Block #558,842

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/23/2014, 7:54:12 PM Β· Difficulty 10.9640 Β· 6,235,622 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dd08d5f2b290430aa34e096c71bf633ea774e1ff337b9565ccf78691dda1a21e
View on Chainz β†—

Height

#558,842

Difficulty

10.964012

Transactions

1

Size

208 B

Version

2

Bits

0af6c976

Nonce

1,905,000,296

Timestamp

5/23/2014, 7:54:12 PM

Confirmations

6,235,622

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6cfc7ece78cb5bac3b479a26e1e88de9e4f1d85af23e47e70b70951e57b24429
Transactions (1)
Coinbase6cfc7ece78cb5b…70951e57b24429
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.981 Γ— 10⁹⁹(100-digit number)
19817269461821497771…57909851093529336319
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
1.981 Γ— 10⁹⁹(100-digit number)
19817269461821497771…57909851093529336319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.981 Γ— 10⁹⁹(100-digit number)
19817269461821497771…57909851093529336321
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
3.963 Γ— 10⁹⁹(100-digit number)
39634538923642995542…15819702187058672639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.963 Γ— 10⁹⁹(100-digit number)
39634538923642995542…15819702187058672641
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
7.926 Γ— 10⁹⁹(100-digit number)
79269077847285991084…31639404374117345279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.926 Γ— 10⁹⁹(100-digit number)
79269077847285991084…31639404374117345281
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
1.585 Γ— 10¹⁰⁰(101-digit number)
15853815569457198216…63278808748234690559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.585 Γ— 10¹⁰⁰(101-digit number)
15853815569457198216…63278808748234690561
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
3.170 Γ— 10¹⁰⁰(101-digit number)
31707631138914396433…26557617496469381119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.170 Γ— 10¹⁰⁰(101-digit number)
31707631138914396433…26557617496469381121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 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
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 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:57,599,754 XPMΒ·at block #6,794,463 Β· updates every 60s
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