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Block #211,548

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/15/2013, 6:41:21 PM Β· Difficulty 9.9165 Β· 6,594,263 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
da160e119fe8acb43054632bdf9cc47a800f5ccb22368cf91e785958cffc78dd
View on Chainz β†—

Height

#211,548

Difficulty

9.916547

Transactions

1

Size

198 B

Version

2

Bits

09eaa2d0

Nonce

121,070

Timestamp

10/15/2013, 6:41:21 PM

Confirmations

6,594,263

Mined by

⛏️ P2SHAHnBbSZUB33VknNc1hSqs87dGJRVfat6WW

Merkle Root

f20d6a1f5ab8f0f9024616cf70a327dfaaac31a5a25d6f5b2501445c9f6dde5f
Transactions (1)
Coinbasef20d6a1f5ab8f0…01445c9f6dde5f
1 in β†’ 1 out10.1500 XPM109 B
AHnBbSZU…RVfat6WW
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.

2.280 Γ— 10⁹²(93-digit number)
22803885704588500694…94292627138991346559
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
2.280 Γ— 10⁹²(93-digit number)
22803885704588500694…94292627138991346559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.280 Γ— 10⁹²(93-digit number)
22803885704588500694…94292627138991346561
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
4.560 Γ— 10⁹²(93-digit number)
45607771409177001389…88585254277982693119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.560 Γ— 10⁹²(93-digit number)
45607771409177001389…88585254277982693121
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
9.121 Γ— 10⁹²(93-digit number)
91215542818354002778…77170508555965386239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.121 Γ— 10⁹²(93-digit number)
91215542818354002778…77170508555965386241
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
1.824 Γ— 10⁹³(94-digit number)
18243108563670800555…54341017111930772479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.824 Γ— 10⁹³(94-digit number)
18243108563670800555…54341017111930772481
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
3.648 Γ— 10⁹³(94-digit number)
36486217127341601111…08682034223861544959
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:57,690,574 XPMΒ·at block #6,805,810 Β· updates every 60s
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