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Block #1,663,429

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/7/2016, 6:04:56 PM Β· Difficulty 10.7229 Β· 5,161,170 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
70b9dd4cb41d32a9d02a16795b08c550adb3002e7f010bc3830caa2d4c4d11a4
View on Chainz β†—

Height

#1,663,429

Difficulty

10.722913

Transactions

1

Size

200 B

Version

2

Bits

0ab910cd

Nonce

337,093,104

Timestamp

7/7/2016, 6:04:56 PM

Confirmations

5,161,170

Mined by

⛏️ P2SHAUDSUaABfEJhmjAHFDvvygtZkkvooFHFDW

Merkle Root

a7e0a5792987b48464a14ad4cf7368e870ed18a09557b1868284f35f38f0b073
Transactions (1)
Coinbasea7e0a5792987b4…84f35f38f0b073
1 in β†’ 1 out8.6800 XPM109 B
AUDSUaAB…vooFHFDW
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.

3.193 Γ— 10⁹⁷(98-digit number)
31939245971591290849…29498452587396423679
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
3.193 Γ— 10⁹⁷(98-digit number)
31939245971591290849…29498452587396423679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.193 Γ— 10⁹⁷(98-digit number)
31939245971591290849…29498452587396423681
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
6.387 Γ— 10⁹⁷(98-digit number)
63878491943182581698…58996905174792847359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.387 Γ— 10⁹⁷(98-digit number)
63878491943182581698…58996905174792847361
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
1.277 Γ— 10⁹⁸(99-digit number)
12775698388636516339…17993810349585694719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.277 Γ— 10⁹⁸(99-digit number)
12775698388636516339…17993810349585694721
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
2.555 Γ— 10⁹⁸(99-digit number)
25551396777273032679…35987620699171389439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.555 Γ— 10⁹⁸(99-digit number)
25551396777273032679…35987620699171389441
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
5.110 Γ— 10⁹⁸(99-digit number)
51102793554546065358…71975241398342778879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.110 Γ— 10⁹⁸(99-digit number)
51102793554546065358…71975241398342778881
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:57,840,861 XPMΒ·at block #6,824,598 Β· updates every 60s
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