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Block #1,534,417

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 5:31:44 AM Β· Difficulty 10.6177 Β· 5,292,738 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
16de19ec41e28effb78a1f60ce97df9876b46de69c4e9f9c2e278d172679e563
View on Chainz β†—

Height

#1,534,417

Difficulty

10.617691

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e2101

Nonce

374,207,208

Timestamp

4/10/2016, 5:31:44 AM

Confirmations

5,292,738

Mined by

⛏️ P2SHATxR7cjPvs9Tu9pYoawmcjtwVWtyJgmWp2

Merkle Root

b95885c980889b847442420c2e8463e138d765da3cc25125cc2bbb64fc73f5c3
Transactions (2)
Coinbase8044b18694a6e5…a0ef2ebc22a8c2
1 in β†’ 1 out8.9400 XPM110 B
ATxR7cjP…tyJgmWp2
3fe075f9a3421d…bfe6a3a3622783
51 in β†’ 1 out1107.8066 XPM7.42 KB
ARX2FgWe…1CahKXLH
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.

1.046 Γ— 10⁹⁡(96-digit number)
10463414994048866136…00539933032348344319
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
1.046 Γ— 10⁹⁡(96-digit number)
10463414994048866136…00539933032348344319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.046 Γ— 10⁹⁡(96-digit number)
10463414994048866136…00539933032348344321
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
2.092 Γ— 10⁹⁡(96-digit number)
20926829988097732273…01079866064696688639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.092 Γ— 10⁹⁡(96-digit number)
20926829988097732273…01079866064696688641
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
4.185 Γ— 10⁹⁡(96-digit number)
41853659976195464547…02159732129393377279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.185 Γ— 10⁹⁡(96-digit number)
41853659976195464547…02159732129393377281
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
8.370 Γ— 10⁹⁡(96-digit number)
83707319952390929095…04319464258786754559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.370 Γ— 10⁹⁡(96-digit number)
83707319952390929095…04319464258786754561
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
1.674 Γ— 10⁹⁢(97-digit number)
16741463990478185819…08638928517573509119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.674 Γ— 10⁹⁢(97-digit number)
16741463990478185819…08638928517573509121
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:57,861,424 XPMΒ·at block #6,827,154 Β· updates every 60s
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