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Block #1,544,281

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/16/2016, 5:51:06 PM Β· Difficulty 10.6531 Β· 5,268,702 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
db6e7405b8bcc44fc7d5210891b95d4edd52f09a7e7af30e4f64da4ca451a91a
View on Chainz β†—

Height

#1,544,281

Difficulty

10.653132

Transactions

1

Size

201 B

Version

2

Bits

0aa733a3

Nonce

491,052,284

Timestamp

4/16/2016, 5:51:06 PM

Confirmations

5,268,702

Mined by

⛏️ P2SHATc3aKXMBEpVPniE9p1UHVhv6f4ToZq2ap

Merkle Root

da09c9c24aa1ce9c457eb72bf9d4b8c48291b9b6a0ccfb9b398205d9f908924e
Transactions (1)
Coinbaseda09c9c24aa1ce…8205d9f908924e
1 in β†’ 1 out8.8000 XPM110 B
ATc3aKXM…4ToZq2ap
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.

1.709 Γ— 10⁹⁢(97-digit number)
17095424572257922605…73968945524943257599
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
1.709 Γ— 10⁹⁢(97-digit number)
17095424572257922605…73968945524943257599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.709 Γ— 10⁹⁢(97-digit number)
17095424572257922605…73968945524943257601
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
3.419 Γ— 10⁹⁢(97-digit number)
34190849144515845211…47937891049886515199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.419 Γ— 10⁹⁢(97-digit number)
34190849144515845211…47937891049886515201
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
6.838 Γ— 10⁹⁢(97-digit number)
68381698289031690422…95875782099773030399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.838 Γ— 10⁹⁢(97-digit number)
68381698289031690422…95875782099773030401
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
1.367 Γ— 10⁹⁷(98-digit number)
13676339657806338084…91751564199546060799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.367 Γ— 10⁹⁷(98-digit number)
13676339657806338084…91751564199546060801
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
2.735 Γ— 10⁹⁷(98-digit number)
27352679315612676168…83503128399092121599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.735 Γ— 10⁹⁷(98-digit number)
27352679315612676168…83503128399092121601
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:57,747,901 XPMΒ·at block #6,812,982 Β· updates every 60s
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