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Block #2,248,045

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/12/2017, 9:18:02 AM Β· Difficulty 10.9477 Β· 4,595,169 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2a1d43caf7ccf24302c652bb38842e87a84feb059125fd10017ab2ac2a56d3eb
View on Chainz β†—

Height

#2,248,045

Difficulty

10.947663

Transactions

2

Size

1.57 KB

Version

2

Bits

0af29a0b

Nonce

1,073,191,828

Timestamp

8/12/2017, 9:18:02 AM

Confirmations

4,595,169

Mined by

⛏️ P2SHAebdyqd8ph8Z3G5zqvaP3JQbzbiu2aKpzf

Merkle Root

b97b6ddc633b8eacfeaea7b194c4f4255e97e61f5abe46d5b73038b7059418d2
Transactions (2)
Coinbasef78d01b7c54fc2…a0dfdef76c074a
1 in β†’ 1 out8.3500 XPM110 B
Aebdyqd8…iu2aKpzf
22248a77b05f1d…9524b02e3d3a9f
9 in β†’ 2 out2036.1157 XPM1.38 KB
AQj222dt…P7KkzW4nARaNCeSx…b8M3uhxY
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.

6.842 Γ— 10⁹⁡(96-digit number)
68424989098985449197…75744346102287249919
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
6.842 Γ— 10⁹⁡(96-digit number)
68424989098985449197…75744346102287249919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.842 Γ— 10⁹⁡(96-digit number)
68424989098985449197…75744346102287249921
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
1.368 Γ— 10⁹⁢(97-digit number)
13684997819797089839…51488692204574499839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.368 Γ— 10⁹⁢(97-digit number)
13684997819797089839…51488692204574499841
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
2.736 Γ— 10⁹⁢(97-digit number)
27369995639594179679…02977384409148999679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.736 Γ— 10⁹⁢(97-digit number)
27369995639594179679…02977384409148999681
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
5.473 Γ— 10⁹⁢(97-digit number)
54739991279188359358…05954768818297999359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.473 Γ— 10⁹⁢(97-digit number)
54739991279188359358…05954768818297999361
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
1.094 Γ— 10⁹⁷(98-digit number)
10947998255837671871…11909537636595998719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.094 Γ— 10⁹⁷(98-digit number)
10947998255837671871…11909537636595998721
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:57,990,085 XPMΒ·at block #6,843,213 Β· updates every 60s
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