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Block #2,045,983

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/31/2017, 2:04:14 AM Β· Difficulty 10.6833 Β· 4,795,151 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9add0909cf0c1d21186f76641c4fbda8ff3ad0c8a5eef8952e6d263522f106cb
View on Chainz β†—

Height

#2,045,983

Difficulty

10.683288

Transactions

1

Size

200 B

Version

2

Bits

0aaeebf4

Nonce

1,553,445,374

Timestamp

3/31/2017, 2:04:14 AM

Confirmations

4,795,151

Mined by

⛏️ P2SHAMrFnossgsXhXHWf5TKUivaKAPwR6CUgQe

Merkle Root

06a9afb54a7f90cb730031d24559a0a57670705e89ae4e85347b357a7f49aa13
Transactions (1)
Coinbase06a9afb54a7f90…7b357a7f49aa13
1 in β†’ 1 out8.7500 XPM109 B
AMrFnoss…wR6CUgQe
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.

8.947 Γ— 10⁹⁢(97-digit number)
89477972470051725312…62778694693191782399
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
8.947 Γ— 10⁹⁢(97-digit number)
89477972470051725312…62778694693191782399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.947 Γ— 10⁹⁢(97-digit number)
89477972470051725312…62778694693191782401
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
1.789 Γ— 10⁹⁷(98-digit number)
17895594494010345062…25557389386383564799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.789 Γ— 10⁹⁷(98-digit number)
17895594494010345062…25557389386383564801
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
3.579 Γ— 10⁹⁷(98-digit number)
35791188988020690125…51114778772767129599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.579 Γ— 10⁹⁷(98-digit number)
35791188988020690125…51114778772767129601
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
7.158 Γ— 10⁹⁷(98-digit number)
71582377976041380250…02229557545534259199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.158 Γ— 10⁹⁷(98-digit number)
71582377976041380250…02229557545534259201
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
1.431 Γ— 10⁹⁸(99-digit number)
14316475595208276050…04459115091068518399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.431 Γ— 10⁹⁸(99-digit number)
14316475595208276050…04459115091068518401
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:57,973,442 XPMΒ·at block #6,841,133 Β· updates every 60s
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