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Block #2,144,046

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2017, 7:08:33 PM Β· Difficulty 10.8832 Β· 4,687,593 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
38a2d5f7078b77c6b2994f6b04c139b25c094a4364707301e9baa0e685a9db4d
View on Chainz β†—

Height

#2,144,046

Difficulty

10.883246

Transactions

1

Size

200 B

Version

2

Bits

0ae21c6d

Nonce

1,739,350,270

Timestamp

6/3/2017, 7:08:33 PM

Confirmations

4,687,593

Mined by

⛏️ P2SHAa3sKuNqRTxz67eJapMXf8aBGa2jeSHKQj

Merkle Root

6441a60b28c129b7f6eadafa6123de9f8b179ce9b074079cc43700568ad8a08f
Transactions (1)
Coinbase6441a60b28c129…3700568ad8a08f
1 in β†’ 1 out8.4300 XPM109 B
Aa3sKuNq…2jeSHKQj
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.

2.150 Γ— 10⁹⁷(98-digit number)
21502831904833594296…24884757106068029439
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
2.150 Γ— 10⁹⁷(98-digit number)
21502831904833594296…24884757106068029439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.150 Γ— 10⁹⁷(98-digit number)
21502831904833594296…24884757106068029441
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
4.300 Γ— 10⁹⁷(98-digit number)
43005663809667188593…49769514212136058879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.300 Γ— 10⁹⁷(98-digit number)
43005663809667188593…49769514212136058881
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
8.601 Γ— 10⁹⁷(98-digit number)
86011327619334377187…99539028424272117759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.601 Γ— 10⁹⁷(98-digit number)
86011327619334377187…99539028424272117761
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
1.720 Γ— 10⁹⁸(99-digit number)
17202265523866875437…99078056848544235519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.720 Γ— 10⁹⁸(99-digit number)
17202265523866875437…99078056848544235521
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
3.440 Γ— 10⁹⁸(99-digit number)
34404531047733750874…98156113697088471039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.440 Γ— 10⁹⁸(99-digit number)
34404531047733750874…98156113697088471041
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:57,897,216 XPMΒ·at block #6,831,638 Β· updates every 60s
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