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Block #2,136,747

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2017, 10:52:54 AM Β· Difficulty 10.8919 Β· 4,681,031 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c76a59d7c69dad5e93d8f7f94bc2c376119dc372fcccbddc133067db773230de
View on Chainz β†—

Height

#2,136,747

Difficulty

10.891916

Transactions

2

Size

688 B

Version

2

Bits

0ae4549f

Nonce

76,947,967

Timestamp

5/29/2017, 10:52:54 AM

Confirmations

4,681,031

Mined by

⛏️ P2SHAb15iz3FDPajYrhx9Am1HPaowvNUByNbLv

Merkle Root

3372424d6bc5223fb34795780d9240c14582b55c458eec1967b3cf1693f9a1cf
Transactions (2)
Coinbase13d3d8c3a28d1d…7bae95f885446b
1 in β†’ 1 out8.4300 XPM109 B
Ab15iz3F…NUByNbLv
65b6c4ff9c4733…c925fd757df05e
3 in β†’ 1 out316.8546 XPM489 B
AG2svXci…QmEdARd8
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.

5.228 Γ— 10⁹⁴(95-digit number)
52283241467030731745…29771250371508889599
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
5.228 Γ— 10⁹⁴(95-digit number)
52283241467030731745…29771250371508889599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.228 Γ— 10⁹⁴(95-digit number)
52283241467030731745…29771250371508889601
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
1.045 Γ— 10⁹⁡(96-digit number)
10456648293406146349…59542500743017779199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.045 Γ— 10⁹⁡(96-digit number)
10456648293406146349…59542500743017779201
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
2.091 Γ— 10⁹⁡(96-digit number)
20913296586812292698…19085001486035558399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.091 Γ— 10⁹⁡(96-digit number)
20913296586812292698…19085001486035558401
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
4.182 Γ— 10⁹⁡(96-digit number)
41826593173624585396…38170002972071116799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.182 Γ— 10⁹⁡(96-digit number)
41826593173624585396…38170002972071116801
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
8.365 Γ— 10⁹⁡(96-digit number)
83653186347249170793…76340005944142233599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.365 Γ— 10⁹⁡(96-digit number)
83653186347249170793…76340005944142233601
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:57,786,282 XPMΒ·at block #6,817,777 Β· updates every 60s
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