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Block #1,610,541

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/2/2016, 4:52:09 AM Β· Difficulty 10.6092 Β· 5,231,610 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7c341df61d22c13b035fb4dcd63fe482e48aabb5ea819f8895aa7bec909773ac
View on Chainz β†—

Height

#1,610,541

Difficulty

10.609155

Transactions

1

Size

199 B

Version

2

Bits

0a9bf198

Nonce

139,826,060

Timestamp

6/2/2016, 4:52:09 AM

Confirmations

5,231,610

Mined by

⛏️ P2SHAJzABwX8ugRT3VNc2VhAFuKjFk19bEDQ8t

Merkle Root

9efcfe6d898807f799b0e0b1c54425f84bbcc305cff8038e299a1a6286d5a8fd
Transactions (1)
Coinbase9efcfe6d898807…9a1a6286d5a8fd
1 in β†’ 1 out8.8700 XPM109 B
AJzABwX8…19bEDQ8t
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.

5.734 Γ— 10⁹⁡(96-digit number)
57342864795243660797…08379690440080586879
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
5.734 Γ— 10⁹⁡(96-digit number)
57342864795243660797…08379690440080586879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.734 Γ— 10⁹⁡(96-digit number)
57342864795243660797…08379690440080586881
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
1.146 Γ— 10⁹⁢(97-digit number)
11468572959048732159…16759380880161173759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.146 Γ— 10⁹⁢(97-digit number)
11468572959048732159…16759380880161173761
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
2.293 Γ— 10⁹⁢(97-digit number)
22937145918097464319…33518761760322347519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.293 Γ— 10⁹⁢(97-digit number)
22937145918097464319…33518761760322347521
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
4.587 Γ— 10⁹⁢(97-digit number)
45874291836194928638…67037523520644695039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.587 Γ— 10⁹⁢(97-digit number)
45874291836194928638…67037523520644695041
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
9.174 Γ— 10⁹⁢(97-digit number)
91748583672389857276…34075047041289390079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.174 Γ— 10⁹⁢(97-digit number)
91748583672389857276…34075047041289390081
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:57,981,597 XPMΒ·at block #6,842,150 Β· updates every 60s
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