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Block #204,417

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/11/2013, 11:56:20 AM Β· Difficulty 9.8985 Β· 6,601,446 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
836bb3daf92ce45b24b5bbcc0c58078ddd9478d28f55b31618e64081a2607f2d
View on Chainz β†—

Height

#204,417

Difficulty

9.898490

Transactions

2

Size

390 B

Version

2

Bits

09e60370

Nonce

29,180

Timestamp

10/11/2013, 11:56:20 AM

Confirmations

6,601,446

Mined by

⛏️ P2SHAUtR5tdmmyLmJWJAHikCLp6qqTGSCA2FvY

Merkle Root

b5454a514e384089a6168cfc5dbeae9104137c6b3cc273c3afb24efbaa195ac6
Transactions (2)
Coinbase6defca1f352897…a18733c19c7f22
1 in β†’ 1 out10.2000 XPM109 B
AUtR5tdm…GSCA2FvY
6bc2bf786466f3…0390a3a59cbf7b
1 in β†’ 1 out29.9900 XPM192 B
AYCx2iSF…qsZ4cJTM
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.

6.229 Γ— 10⁹¹(92-digit number)
62297387162813769233…97273294030953658239
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
6.229 Γ— 10⁹¹(92-digit number)
62297387162813769233…97273294030953658239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.229 Γ— 10⁹¹(92-digit number)
62297387162813769233…97273294030953658241
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
1.245 Γ— 10⁹²(93-digit number)
12459477432562753846…94546588061907316479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.245 Γ— 10⁹²(93-digit number)
12459477432562753846…94546588061907316481
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
2.491 Γ— 10⁹²(93-digit number)
24918954865125507693…89093176123814632959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.491 Γ— 10⁹²(93-digit number)
24918954865125507693…89093176123814632961
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
4.983 Γ— 10⁹²(93-digit number)
49837909730251015386…78186352247629265919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.983 Γ— 10⁹²(93-digit number)
49837909730251015386…78186352247629265921
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
9.967 Γ— 10⁹²(93-digit number)
99675819460502030772…56372704495258531839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.967 Γ— 10⁹²(93-digit number)
99675819460502030772…56372704495258531841
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:57,690,986 XPMΒ·at block #6,805,862 Β· updates every 60s
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